Title
Author(s)
Citation
Issue Date
Time-of-flight measurements of charge carrier diffusion in
In_xGa_[1-x]N/GaN quantum wells
Danhof, J.; Schwarz, U. T.; Kaneta, A.; Kawakami, Y.
PHYSICAL REVIEW B (2011), 84(3)
2011-07
URL
http://hdl.handle.net/2433/161772
Right
©2011 American Physical Society
Type
Journal Article
Textversion
publisher
Kyoto University
PHYSICAL REVIEW B 84, 035324 (2011)
Time-of-flight measurements of charge carrier diffusion in In x Ga1−x N/GaN quantum wells
J. Danhof* and U. T. Schwarz
Fraunhofer Institute for Applied Solid State Physics IAF, Tullastraße 72, D-79108 Freiburg, Germany and
Albert-Ludwigs-Universität Freiburg, IMTEK, Georges-Köhler-Allee 106, D-79110 Freiburg, Germany
A. Kaneta and Y. Kawakami
Kyoto University, Katsura Campus, Nishikyo-ku, Kyoto 615-2312, Japan
(Received 19 April 2011; revised manuscript received 10 May 2011; published 29 July 2011)
Time-of-flight experiments were performed to investigate charge carrier diffusion in InGaN quantum wells. A
mere optical setup with high spatial resolution was established on the basis of confocal microphotoluminescence
microscopy in order to measure charge carrier movement directly. We investigate a multiquantum well sample
emitting light at about 510 nm and found an ambipolar lateral diffusion constant of 0.25 ± 0.05 cm2 /s.
DOI: 10.1103/PhysRevB.84.035324
PACS number(s): 73.50.Gr, 73.61.Ey, 78.47.da, 78.55.Bq
Indium gallium nitride (InGaN) is a material system that
has proven to be very applicable for all kinds of semiconductor
devices. Research has also found the system to be very
interesting from a physical point of view. InGaN/GaN quantum
wells (QWs) are known to suffer from a very large number
of threading dislocations1,2 and material inhomogeneities3
due to growth on foreign substrates, strain, and solid phase
immiscibility.4 The larger the indium content in the QW is
the stronger the effects of these inhomogeneities become.5,6
Photoluminescence microscopy of such light emitting QWs
show therefore fluctuations of intensity, energy, and full width
at half maximum (FWHM) across the sample on different
length scales.5,7 A lot of research has been dedicated to
understand why QWs with such a low quality compared
to, e.g., GaAs/AlGaAs QWs nevertheless emit light, even
stimulated emission. Localization of charge carriers provides
one explanation.8–10 Charge carriers are localized in minima
of the energy landscape of the QW and thus prevented
from traveling to nonradiative recombination centers. In this
context, a carrier diffusion length of the order of tens of
nanometers is expected in the low carrier density regime.
Another possibility is that the charge carriers are prevented
from reaching nonradiative recombination centers by potential
barriers.11,12 We found direct evidence of lateral charge carrier
transport in InGaN QWs. In this article, we describe these
measurements with our time-of-flight setup.
On the basis of an idea by Hillmer et al. from more
than 20 years ago,13 we created a setup for time-of-flight
experiments that is precise enough to measure the small
lateral diffusion coefficient in InGaN/GaN QWs. For this
purpose, we modified a confocal microscope previously used
for microphotoluminescence measurements (see Fig. 1). The
spatial resolution of this confocal microscope is better than
400 nm. The pinhole of the confocal setup, in our case a
single mode optical fiber, was attached to a scanning stage
to allow for x–y scans of the microscope’s image plane.
We call this technique pinhole scan.14 This way, we can excite
the sample by focusing a laser beam onto the sample, as one
would for conventional confocal microscopy. By scanning
the image plane, we can closely analyze variation of the
sample’s emission under inhomogeneous illumination, i.e.,
directly at the center of excitation by the laser or in its vicinity
1098-0121/2011/84(3)/035324(5)
where less or no excitation from the laser takes place. The
accuracy of our scanning stage is 10 ± 20 nm which translates
to 0.25 ± 0.5 nm on the sample.
As a source of excitation, we used a picosecond pulsed
frequency doubled Titan Sapphire laser with a pulse picker,
set to a wavelength of 400 nm. For nontime-resolved pinhole
scans, the repetition rate of the laser was 80 MHz and for
detection, a 50 cm spectrometer with a liquid nitrogen cooled
CCD chip was used. For time-of-flight experiments, temporal
resolution has to be added. The repetition rate of the laser was
set to 4 MHz and a streak camera was used for time-resolved
detection. The temporal resolution of the streak camera was
42 ps and the jitter was about 200 ps.
If excitation and detection happen at the same spot
(confocal), the total carrier lifetime is being measured for
samples with low charge carrier diffusion. If excitation and
detection are spatially separated, one can observe a delayed
onset of photoluminescence, corresponding to the time the
carriers need to travel the distance between the locations of
excitation and detection. The confocal technique suppresses
scattered light. These time delays between the excitation of
charge carriers and the detection of their emitted luminescence
can be measured.
For our measurements, we use a green light emitting c-plane
InGaN/GaN multi-QW (MQW) sample grown by Osram Opto
Semiconductors. The MQW structure consists of seven 3 nm
thick QWs with an indium content of about 26%, separated by
nominally undoped GaN barriers. The QWs are covered by a
10 nm thick GaN cap layer. The whole structure was grown
on a GaN substrate to create a sample with a low threading
dislocation density.15 The threading dislocation density is 5 ×
107 cm−2 . This low threading dislocation density allows us
to find large enough dislocation free areas to perform our
experiment.
Lateral transport of charge carriers can be described by a
continuity equation:16
∂n
n
+ Dn ⊥ n,
= Gn −
∂t
τn
(1)
where diffusion is taken into account in the two-dimensional
plane of the QW. n represents the number of charge carriers
and Gn represents their generation rate. τn is the charge carrier
035324-1
©2011 American Physical Society
y
Δy=0 nm
x
tube lense
Δy=900 nm
0.8
enough to take a significant influence on the motion of charge
carriers in our sample. The effect of drift is thus neglected.
However, the strong QCSE in green light emitting QWs creates
long radiative charge carrier life times which is favorable for
our experiment.
We describe the spatial distribution of the excitation density
by the laser pulse on the sample by a Gaussian. Therefore, we
also describe the created charge carrier density in the QW by
a Gaussian, assuming that the dependence of the generation
rate Gn on the excitation density is an infinitely differentiable
function. The shape of the charge carrier distribution in the
sample at the time of excitation (t = 0 ns) provides a boundary
condition:
n=e
0.6
0.4
Δy=0 nm
0.2
0
0
sample
2
4
6
8
time [ns]
10 12
Δy=900 nm
FIG. 1. (Color online) Experimental setup. The sample is excited
by a laser beam focused with a microscope objective. In the pinhole
plane, we observe a magnified image of the photoluminescence
light from the sample. With a pinhole, we can thus select points
of observation on the sample and analyze their temporal behavior
with a streak camera. In the example, the distance between points of
excitation and detection is 900 nm.
life time and Dn is the charge carrier diffusion constant. ⊥
is the 2D Laplace operator. In our case, the generation rate Gn
is zero after the excitation of the sample through a picosecond
laser pulse. The differential equation is independent from the
type of charge carriers that are observed and thus appropriate to
describe ambipolar transport, i.e., the motion of an electronhole cloud interacting via Coulomb forces17 as well as the
motion of excitons. This suits our experiment well as we
can only observe recombining electrons and holes. There
are indications that in a QW structure such as ours at room
temperature excitons already dissociate into electron-hole
pairs.18 With our experiment, we cannot distinguish between
the two.
In this model, we are neglecting drift. When charge carriers
are created in a c-plane InGaN/GaN QW structure, they reduce
the quantum confined Stark effect (QCSE) by shielding the
piezoelectric field which implicates a blueshift of the emission.
The reduction of the QCSE together with the blueshift depends
on the charge carrier density present in the QW. When we
excite our sample locally, we therefore also induce a field
within the plane of the QW which will cause drift overlaid
with diffusion. The maximum of the electric field in the plane
of the QW structure average over time was determined from
the lateral energy shift to be 740 ± 20 V/cm. Measurements
with continuous wave excitation at the same sample suggest
that at very high excitation densities, the internal lateral electric
field might become as high as 1.4 kV/cm. Drift caused by an
accordant electric field can be integrated into the diffusion
equation [Eq. (1)]. It was found that the field is not strong
(− x
2 +y 2
2re2
)
(2)
.
Parameters to be determined from the measurement are τn ,
re , and Dn . The resulting differential equation can be solved
numerically.
We excite our sample at a wavelength of 400 nm. Charge
carriers are only created resonantly in the MQW and not in
the barriers. Therefore, all observed diffusion effects are due
to charge carrier dynamics in the QW structure only. The
assumption is made that all QWs contain the same charge
carrier densities.19 We performed our measurements in the
regime of high excitation density of the curve of the internal
quantum efficiency (IQE) which is relevant for operating light
emitting diodes and laser diodes. The actual charge carrier
density in the sample at the time of excitation was estimated
by measuring its IQE. An excitation density dependent IQE
curve can be fitted with a third-order polynomial describing
recombination mechanisms in InGaN/GaN optical devices.
This model is known as ABC model.20 From the fitting
parameters A (Shockley-Read-Hall recombination, a nonradiative single-particle process), B (radiative recombination, a
two-particle process), and C (Auger recombination, a threeparticle nonradiative process), the number of charge carriers
in the QWs can be estimated. This is shown in Fig. 2. The
peak charge carrier density in our measurement is roughly
0.08
internal quantum efficiency
intensity norm.
microscope
objective
1
PHYSICAL REVIEW B 84, 035324 (2011)
0.06
Fit parameters:
A = 5.3·10-2 ns-1
B = 6.5·10-6 cm2 s-1
C = 3.0·10-17 cm4s-1
0.04
0.02
carriers:
1.3·1012 cm-2
6.5·1012 cm-2
0
0.1
1
10
100
excitation density (cw) [kW/cm2 ]
measurement
beam
splitter
Δy=900 nm
pinhole
excitation
laser pulse
J. DANHOF, U. T. SCHWARZ, A. KANETA, AND Y. KAWAKAMI
1000
FIG. 2. Excitation dependent internal quantum efficiency. The
gray dashed continuous line was determined from continuous wave
excitation. The dots were derived from pulsed excitation. The gray
continuous line resembles a fit with the fitting parameters given in the
image. The peak charge carrier density in our experiment can thus be
estimated to be about 6.5 × 1012 cm−2 .
035324-2
PHYSICAL REVIEW B 84, 035324 (2011)
1
TIME-OF-FLIGHT MEASUREMENTS OF CHARGE CARRIER . . .
450
(b)
3
2
1
wavelength [nm]
470
0.75
0.5
0.25
intensity [arb. units]
position y [µm]
4
(a)
490
510
530
550
0
0
0
0
1
2
3
position x [µm]
4
FIG. 3. (Color) Nontime-resolved pinhole scan of an InGaN
MQW sample for orientation on the sample. The colored circles mark
points where time-resolved measurements were taken. The dashes
circle marks the FWHM of the laser spot at y = 360 ± 10 nm.
6.5 × 1012 cm−2 . Taking the Mott density to be of the order21
of 1/π a02 , with a Bohr radius a0 of 2.5 nm, we find that our
charge carrier density is approximately the Mott density for
bulk material.
We performed nontime-resolved pinhole scans in the immediate vicinity of the excitation spot to allow for orientation
on the sample. The result is an intensity map as displayed
in Fig. 3. The figure shows an image of the sample, the
position of the exciting laser spot at the center. The bright
area in the middle of the image caused by the exciting laser
focus is not concentrical as would be expected. This is due
to inhomogeneity of the sample already stated above. On
this nontime-resolved scan, it is impossible to distinguish
between charge carriers that recombine within the area that
is hit by the laser and charge carriers that diffused away from
the center of excitation and recombined there at a later time.
For our measurements, we choose a spot within a particularly
bright area to ensure a large signal-to-noise ratio and avoid
threading dislocations and an unnecessary large number of
point defects. Measurements within or in the vicinity of areas
which appear dark in microphotoluminescence scans have also
been performed. We observe a change in the signal’s intensity
rather than the diffusion constant.
To measure the charge carrier diffusion constant, a line scan
from the center of excitation to the vicinity was performed. The
scanning points for time-resolved pinhole scans are marked by
colored circles in Fig. 3. Streak camera images of the actual
time-resolved measurements are depicted in Fig. 4. Figure 4(a)
was taken with matching excitation and detection position
(y = 0). It shows directly the decay of intensity at the
center of excitation after the laser pulse. At short wavelengths
(450–475 nm), the signal decays very fast. The fact that this
part of the emission is blueshifted very strongly and is only
present at the highest excitation densities indicates that this is
already stimulated emission from the QW. Analysis of InGaN
laser diode performance just below lasing threshold has shown
2
4
6 8 10 12 14 0
time [ns]
2
4
6 8 10 12 14
time [ns]
FIG. 4. (Color) Time-resolved spectra from time-resolved pinhole scans. (a) y = 0 nm. Position of detection is the red circle in
Fig. 3. (b) y = 675 nm. Position of detection is the blue circle in
Fig. 3. The color scaling was matched for good visible recognition.
The maximum intensity of the measurement on the left side is a factor
14 larger than on the right side.
that there is already stimulated emission before actual lasing
starts.20,22 The shift in wavelength from 475 nm to longer
wavelengths depending on the charge carrier density in the
sample is typical for green light emitting InGaN/GaN QW
samples and a consequence of the quantum-confined Stark
effect.
Figure 4(b) depicts time-resolved spectra with a distance of
y = 675 nm between the center of excitation and detection.
This position of detection is marked by a blue circle in Fig. 3.
The emission peak intensity at this detection spot is about
a factor 14 lower when compared to y = 0. The emission
wavelength of the sample is shifted to longer wavelengths
here. This is again a result of the QCSE and the fact that here
the charge carrier density is too low for stimulated emission.
The very short pulse of emission at about 480 nm is due to
scattered light. Most importantly, we observe a delay of the
maximum of the emission intensity after the laser pulse. In
Fig. 4(a), the maximum of the emission sets in directly at the
laser pulse and from this point of time drops constantly. In
Fig. 4(b), there is also emission immediately after excitation.
However, the emission intensity 1 ns after the laser pulse is
larger than directly at the time of excitation.
Time-resolved spectra like these were taken at different
distances between excitation and detection (see the circles of
different colors in Fig. 3). For quantitative analysis, one single
decay line was calculated from the whole time-resolved plot
by integrating from 522 to 534 nm within the whole time
range. The result is shown in Fig. 5. We choose these long
wavelengths to avoid any influence from scattered light or
stimulated emission. A range of 522–534 nm gives us a good
signal-to-noise ratio within the streak camera measurement
while still avoiding disturbing effects. Other wavelength
intervals show same results quantitatively.
The spectra in Fig. 5 can be divided into two groups. The
first group with high intensity has its intensity maximum at t =
0 ns. From this point on, the intensity decays exponentially. All
three spectra were taken within the FWHM of the excitation
035324-3
excess carrier denstiy n [arb. units]
J. DANHOF, U. T. SCHWARZ, A. KANETA, AND Y. KAWAKAMI
TABLE I. Several literature values for diffusion constants of bulk
GaAs, GaAs/AlGaAs quantum well, bulk GaN, and InGaN/GaN
quantum well samples for comparison with our measurement results.
1
distance from center of excitation:
0.8
0 nm
112 nm
225 nm
450 nm
675 nm
900 nm
0.6
0.4
PHYSICAL REVIEW B 84, 035324 (2011)
Sample
Bulk GaAsa
GaAs/AlGaAs quantum wellb
Bulk GaNc
50 nm InGaN layerd
InGaN/GaN quantum wellse
0.2
Diffusion constant (cm2 /s)
20
56
From 1.6 to 2.0
2.1
From 0.51 to 0.62
a
0
0
2
4
6
time [ns]
8
10
12
FIG. 5. (Color) Carrier density as a function of time at different
radii. The intensity profile for different distances between excitation
and detection over time is plotted. The measured curves are compared
to the calculated curves (thick continuous lines).
laser spot. Within this area, obviously no charge carrier
diffusion can be detected. The second group forms spectra
at a distance of 450 nm between excitation and detection
where the shape of the intensity decay over time begins to
change.
These spectra can be used for a quantitative evaluation of
the data. Under the assumption that the charge carrier diffusion
constant is small, the charge carrier life time can be derived
from the spectrum at y = 0. Also, for the spectra that are
relevant for the observation of diffusion (y = 450 nm, y =
675 nm, and y = 900 nm), we find a single exponential
decay of emission intensity with time. In case of this sample,
the radiative charge carrier life time is τn = 16 ± 3 ns. The
other value that needs to be established is the FWHM of the
excitation laser spot. re can be determined from the intensities
of the spectra at t = 0 ns. This position is marked by a vertical
line in Fig. 5. At t = 0 ns, the light emitting area on the sample
has not yet been broadened by diffusion. Since the spatial
position with respect to the excitation center is known for
all intensity decay curves in Fig. 5, the emission intensity
versus position can be fitted by a Gaussian. The FWHM in
case of this setup and this measurement is 720 ± 20 nm, i.e.,
re = 300 ± 9 nm. For illustration, a dashed line is shown in
Fig. 3. The diameter of the circle around the center of excitation
is the FWHM of the laser spot. Now all the parameters needed
to solve Eq. (1) are known, except for the charge carrier
diffusion constant Dn . This last parameter can be determined
by variation. A value of 0.25 ± 0.05 cm2 /s gives, as solutions
of Eq. (1), the continuous lines in Fig. 5. Deviations larger than
±0.05 cm2 /s are in conflict with our measured results and can
be ruled out.
Table I shows an overview over diffusion constants from
different materials and samples. All values listed below were
determined by optical measurements. The diffusion constant
of bulk GaAs was reported23 to be 20 cm2 /s. This is almost
2 orders of magnitude larger than our result. GaAs/AlGaAs
quantum wells display even larger diffusion constants.13 Bulk
GaN was found to have a charge carrier diffusion constant
of 1.6–2.0 cm2 /s depending on the material quality.24–26 This
is about 1 order of magnitude larger than what we found for
Reference 23.
Reference 13.
c
References 24–26.
d
Indium content 8%, Reference 27.
e
Indium content between 22% and 40%, Reference 28.
b
our InGaN/GaN QW. A thick InGaN layer with an indium
content of 8% was reported to show a diffusion constant of
2.1 cm2 /s, which is as large as the reported values for bulk
GaN. For InGaN/GaN QWs, there has been a report28 of
diffusion constants from 0.51 to 0.62 cm2 /s for an indium
content between 22% and 40%.
The significantly larger diffusion constants in
GaAs/AlGaAs QWs compared to InGaN/GaN QWs accounts
for the significantly lower homogeneity of InGaN QWs
compared to GaAs/AlGaAs QWs. For GaAs/AlGaAs QWs,
there have been reports about the influence of QW thickness
on scattering mechanisms and thus charge carrier diffusion
constants. For low temperatures (40–100 K) as well as thin
QWs impurity-interface-roughness and barrier-alloy-disorder
reduce the charge carrier diffusion.29 We expect these
scattering mechanisms to have a much larger influence on
charge carrier diffusions in InGaN/GaN MQWs. This is due to
not only the large number of surfaces within a QW structure,
but also the spontaneous and piezoelectric field, which was
already mentioned above. Electrons and holes are separated
by the electric field, and pushed toward the boundaries. There
even random indium distribution of an otherwise perfectly
grown QW provides roughness at which charge carriers are
scattered.30,31
In conclusion, we performed time-of-flight measurements
to investigate the ambipolar lateral diffusion constant in
InGaN/GaN QWs. To do so, we established a setup for
solely optical measurements. We reconfigurated a confocal
microscope with high spatial resolution to allow for what
we call pinhole scans: the pinhole which defines the area of
detection scanned in the image plane; temporal resolution is
achieved by combining a picosecond Ti : sapphire laser with
a streak camera. With this setup, we directly observed charge
carrier transport in a green light (510 nm) emitting InGaN/GaN
MQW structure. The interpretation of our observations is
confirmed by solving continuity and rate equation specifically
for the measured sample. For the sample discussed in this
work, we were able to determine a charge carrier diffusion
constant of 0.25 ± 0.05 cm2 /s.
The authors would like to thank Japan Society for the
Promotion of Science (JSPS) and Deutsche Forschungsgesellschaft (DFG)(project SCHW 804/8–1) for funding.
035324-4
TIME-OF-FLIGHT MEASUREMENTS OF CHARGE CARRIER . . .
*
julia.danhof@iaf-extern.fraunhofer.de
N. Pauc, M. R. Phillips, V. Aimez, and D. Drouin, Appl. Phys. Lett.
89, 161905 (2006).
2
J. C. Brooksby, J. Mei, and F. A. Ponce, Appl. Phys. Lett. 90,
231901 (2007).
3
T. B. Bartel, C. Kisielowski, P. Specht, T. V. Shubina, V. N. Jmerik,
and S. V. Ivanov, Appl. Phys. Lett. 91, 101908 (2007).
4
I. H. Ho and G. B. Stringfellow, Appl. Phys. Lett. 69, 2701 (1996).
5
B. Han, B. W. Wessels, and M. P. Ulmer, J. Appl. Phys. 99, 084312
(2006).
6
A. Kaneta, M. Funato, and Y. Kawakami, Phys. Rev. B 78, 125317
(2008).
7
H. Masui, T. Melo, J. Sonoda, C. Weisbuch, S. Nakamura, and
S. P. DenBaars, J. Electron. Mater. 39, 15 (2010).
8
S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys.
Lett. 69, 4188 (1996).
9
Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and
S. Nakamura, Appl. Phys. Lett. 70, 981 (1997).
10
J. S. Im, S. Heppel, H. Kollmer, A. Sohmer, J. Off, F. Scholz, and
A. Hangleiter, J. Cryst. Growth 189/190, 597 (1998).
11
S. Sonderegger, E. Feltin, M. Merano, A. Crottini, J. F. Carlin,
B. Deveaud, N. Grandjean, and J. D. Ganière, Appl. Phys. Lett. 89,
232109 (2006).
12
N. K. van der Laak, R. A. Oliver, M. J. Kappers, and C. J.
Humphreys, Appl. Phys. Lett. 90, 121911 (2007).
13
H. Hillmer, A. Forchel, S. Hansmann, E. Lopez, and G. Weimann,
Solid-State Electron. 31, 485 (1988).
14
C. Vierheilig, H. Braun, U. T. Schwarz, W. Wegscheider,
E. Baur, U. Strauß, and V. Härle, Phys. Status Solidi C 4, 2362
(2007).
15
J. Danhof, C. Vierheilig, U. T. Schwarz, T. Meyer, M. Peter,
B. Hahn, M. Meier, and J. Wagner, Phys. Status Solidi C 6, 747
(2009).
16
S. L. Chuang, Physics of Optoelectronic Devices (Wiley, New York,
2009).
1
PHYSICAL REVIEW B 84, 035324 (2011)
17
H. Hillmer, S. Hansmann, A. Forchel, M. Morohashi, E. Lopez,
H. P. Meier, and K. Ploog, Appl. Phys. Lett. 53, 1937 (1988).
18
C. Netzel, V. Hoffmann, T. Wernicke, A. Knauer, M. Weyers,
M. Kneissl, and N. Szabo, J. Appl. Phys. 107, 033510 (2010).
19
D. S. Sizov, R. Bhat, A. Zakharian, J. Napierala, K. Song, D. Allen,
and C. Zah, Appl. Phys. Express 3, 122101 (2010).
20
U. T. Schwarz, Proc. SPIE 7216, 72161U (2009).
21
C.-K. Sun, S. Keller, G. Wang, M. S. Minsky, J. E. Bowers, and
S. P. DenBaars, Appl. Phys. Lett. 69, 1936 (1996).
22
S. Grzanka, P. Perlin, R. Czernecki, L. Marona, M. Boćkowski,
B. Łucznik, M. Leszczyński, and T. Suski, Appl. Phys. Lett. 95,
071108 (2009).
23
B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, Appl.
Phys. Lett. 97, 262119 (2010).
24
T. Malinauskas, K. Jarašiūnas, S. Miasojedovas, S. Juršėnas,
B. Beaumont, and P. Gibart, Appl. Phys. Lett. 88, 202109 (2006).
25
S. M. Olaizola, W. H. Fan, S. A. Hashemizadeh, J.-P. R. Wells,
D. J. Mowbray, M. S. Skolnick, A. M. Fox, and P. J. Parbrook,
Appl. Phys. Lett. 89, 072107 (2006).
26
S. Juršėnas, S. Miasojedovas, A. Žukauskas, B. Łucznik,
I. Grzegory, and T. Suski, Appl. Phys. Lett. 89, 172119 (2006).
27
R. Aleksiejūnas, M. Sūdžius, T. Malinauskas, K. Jarašiūnas,
Q. Fareed, G. Gaska, M. S. Shur, J. Zhang, J. Yang, E. Kuokštis,
and M. A. Khan, Phys. Status Solidi C 7, 2686 (2003).
28
K. Okamoto, A. Kaneta, K. Inoue, Y. Kawakami, M. Terazima,
G. Shinomiya, T. Mukai, and Sg. Fujita, Phys. Status Solidi B 228,
81 (2001).
29
H. Hillmer, A. Forchel, and C. W. Tu, J. Phys. Condens. Matter 5,
5563 (1993).
30
M. Gallart, Y. Morel, T. Taliercio, P. Lefebvre, B. Gil, J. Allègre,
H. Mathieu, N. Grandjean, M. Leroux, and J. Massies, Phys. Status
Solidi A 180, 127 (2000).
31
D. Watson–Parris, M. J. Godfrey, P. Dawson, R. A. Oliver, M. J.
Galtrey, M. J. Kappers, and C. J. Humphreys, Phys. Rev. B 83,
115321 (2011).
035324-5